According to Major League Baseball an official no-hitter consists of a pitcher having pitched at least 9 innings while allowing 0 hits.
In MLB history has a team lost while having a pitcher throw an official no-hitter? If so what were the team(s)?
The same page also notes a loss for a combined no-hitter:
By your question's definition of a no-hitter, the answer would be one game - Ken Johnson's start for the Houston Colt 45s against the Cincinnati Reds.
There have also been four 8 inning efforts that ended short for a full no-hitter due to the fact that the pitcher's team was losing. These were:
It should also be noted that there have been situations where 9 innings of no-hit baseball were pitched, yet the game went into extra innings, where the pitcher ended up earning a loss. Your question is mildly flawed, since it is quoting the original rule. The rule was changed in 1991 to not include games where 9 inning no-hitters were pitched, yet the game was still undecided (source). Other than the previously mentioned situations for Ken Johnson and Baltimore vs. Detroit, there are a few others of note: